194 Lord Rayleigh on Achromatic 



be seen in succession were the parallelism maintained 

 rigorously. 



The achromatism secured by (23) not being absolute, it is 

 of interest to inquire what number of bands are to be ex- 

 pected. The relative retardation of phase, with which we 

 have to deal, is It cos a'/A, or 



2*i/g-/t g sin 8 «) (2?) 



If this be stationary for extra-dense glass and for the line D, 

 we have, as already mentioned, a' = 7 9° 30', and corresponding 

 thereto « = 36° 34/. Taking this as a prescribed value of a, 

 we may compare the values of (27) for the lines C, D, E, 

 using the data given by Hopkinson"*, viz.: — 



C, ^ = 1-644866, \ = '65618xl0- 4 



D, /*= 1-650388, \=-58890xi0- 4 



E, /*= 1-657653, X=*52690x 10~ 4 . 

 We find 



for C (27) = 3036'9x2£, 



D (27) = 3094-5x2£, 



E (27) = 2984-3 x 2*. 



These retardations are reckoned in periods. If we suppose 

 that the retardation for the C-system is just half a period less 

 than for the D-system, we have 



57-6x2*=i; 



so that £= 2J0 cen ^ m - Thus about 27 periods of the D-bands 

 correspond to 26 J of the C-bands. 



If the range of refrangibility contemplated be small, the 

 calculation may conveniently be conducted algebraically. 

 According to Cauchy's law we may replace (27) by 



(28) 



it y/(l-j^sin :i «) (At -A) 



^B •• • • 



Setting fjb = /jL -{-8fi, we have approximately 



(l-/, 2 sin 2 a) (^-A) = (l-/, 2 sin 2 «) fo-A) 

 + S/.{l-^ 2 sin 2 a-2^ sm 2 a) fo-A)} 

 -{8fj,Y{3/ju -A\ sin 2 a + .... 



If a be so chosen that the value of (28) is stationary for /x , 

 the term of the first order in 8/jl vanishes, and we obtain 



* Proc. Eoy. Soc, June 1877. 



